Wow- you guys are definitely pressed for time then.
You should be able to make every target in this game using one firing solution ie: one type of shot. There is no real need to be able to adjust your shot to shoot from anywhere on the field- trying to do so adds a huge amount of un-needed (IMO) complexity. Instead of being able to make all kinds of shots, focus on doing one shot really well (consistently) which can clear the truss, move the ball down the field and hit the high goal. You will learn very fast where the robot needs to be to make each shot and it eliminates having to engineer a complex system on the robot to calculate trajectories etc.
In your situation, I would recommend a spring-loaded catapult. Latex tubing changes in tension and performance over time so use springs for consistency. An arm on a high torque gearmotor to push the catapult into the "cocked" position, engage a latch to hold it there while the cocking arm rotates out of the way, then release the latch when ready. A winch could be used as well that slackens off once cocked to permit firing. The latch could be something as simple as a latch for a chain-link gate (
http://www.plumbersurplus.com/images...132-178772.jpg) actuated by a pneumatic cylinder. All that is required to produce a repeatable shot is open/close the latch, rotate loading arm fwd/rev and two limit switches to stop the arm when the catapult reaches its latching position and when the arm is back in its home position. The entire process of loading can be automated in the program so all the driver needs to do is pull a trigger to shoot- the only logic required is:
If latch limit switch not triggered > rotate loading arm FWD.
If latch limit switch triggered > close latch and rotate loading arm REV
If home limit switch triggered > Stop loading arm.
When driver pulls trigger > Release latch
The driver will quickly learn where the robot needs to be to hit the high goal ie: how far away from the goal- where the trajectory of the ball is flattest to give the greatest tolerance of error. You could also integrate an ultrasonic ranging sensor with a red light/green light system to tell said driver when they are within shooting range.